public void OptimisedStabiliser()
{
// This group is a 3x3 grid with symmetric rows and columns
var group = new PermutationGroup(
new Cycle(new [] { 0, 1 }, new [] { 3, 4 }, new [] { 6, 7 }),
new Cycle(new [] { 0, 1, 2 }, new [] { 3, 4, 5 }, new [] { 6, 7, 8 }),
new Cycle(new [] { 0, 3 }, new [] { 1, 4 }, new [] { 2, 5 }),
new Cycle(new [] { 0, 3, 6 }, new [] { 1, 4, 7 }, new [] { 2, 5, 8 })
);
PermutationGroup stabilisedPointZero;
group.OrbitStabiliser(new Points(0), out stabilisedPointZero);
stabilisedPointZero.Optimise();
Assert.AreEqual(2, stabilisedPointZero.GeneratorCount);
var orbitOfZeroOnStabiliserZero = stabilisedPointZero.Orbit(0);
var orbitOfOneOnStabiliserZero = stabilisedPointZero.Orbit(1);
var orbitOfFourOnStabiliserZero = stabilisedPointZero.Orbit(4);
CollectionAssert.AreEquivalent(new [] { new [] { 0 } }, orbitOfZeroOnStabiliserZero);
CollectionAssert.AreEquivalent(new [] { new [] { 1 }, new [] { 2 } }, orbitOfOneOnStabiliserZero);
CollectionAssert.AreEquivalent(new [] { new [] { 4 }, new [] { 5 }, new [] { 7 }, new [] { 8 } }, orbitOfFourOnStabiliserZero);
}
public void OrbitStabiliser()
{
// This group is a 3x3 grid with symmetric rows and columns
var group = new PermutationGroup(
new Cycle(new [] { 0, 1 }, new [] { 3, 4 }, new [] { 6, 7 }),
new Cycle(new [] { 0, 1, 2 }, new [] { 3, 4, 5 }, new [] { 6, 7, 8 }),
new Cycle(new [] { 0, 3 }, new [] { 1, 4 }, new [] { 2, 5 }),
new Cycle(new [] { 0, 3, 6 }, new [] { 1, 4, 7 }, new [] { 2, 5, 8 })
);
PermutationGroup stabilisedPointZero;
var orbitZero = group.OrbitStabiliser(new Points(0), out stabilisedPointZero);
CollectionAssert.AreEquivalent(Enumerable.Range(0, 9).Select(i => new [] { i }), orbitZero);
var orbitOfZeroOnStabiliserZero = stabilisedPointZero.Orbit(0);
var orbitOfOneOnStabiliserZero = stabilisedPointZero.Orbit(1);
var orbitOfFourOnStabiliserZero = stabilisedPointZero.Orbit(4);
CollectionAssert.AreEquivalent(new [] { new [] { 0 } }, orbitOfZeroOnStabiliserZero);
CollectionAssert.AreEquivalent(new [] { new [] { 1 }, new [] { 2 } }, orbitOfOneOnStabiliserZero);
CollectionAssert.AreEquivalent(new [] { new [] { 4 }, new [] { 5 }, new [] { 7 }, new [] { 8 } }, orbitOfFourOnStabiliserZero);
}
